We study lattice-theoretical extensions of the celebrated Sauer–Shelah–Perles Lemma. We conjecture that a general Sauer–Shelah–Perles Lemma holds for a lattice if and only if the lattice is relatively complemented, and prove partial results towards this conjecture.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics